# Definition:Vector Space Automorphism

## Definition

Let $V$ be a $K$-vector space.

Let $\phi: V \to V$ be a vector space isomorphism to itself.

Then $\phi$ is a vector space automorphism.

## Linguistic Note

The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.

Thus automorphism means self structure.